1. Introduction

1. spatial

2. temporal

   
   

• Spanish neuroscientist (1852–1934), father of modern neuroscience

• Used Golgi stain to map individual neurons

• Proposed the Neuron Doctrine (neurons are separate cells)

• First to describe dendritic spines and growth cones

• Won the 1906 Nobel Prize with Camillo Golgi

• Famous for intricate neuron drawings still used today

• Harvard neuroscientist at the Center for Brain Science

• Pioneer of connectomics (mapping neural circuits)

• Co-developer of Brainbow for colorful neuron imaging

• Uses advanced light and electron microscopy

• Studies how brain circuits form, change, and are wired

• Helps lead large-scale brain mapping efforts

1. Sound Amplitude:

   • Physical change in air pressure

   • Measured in Pascals (Pa) or decibels (dB)

   • Represents loudness

   • Found in acoustic/mechanical systems

2. Voltage:

   • Electrical potential difference

   • Measured in volts (V)

   • Represents signal strength in circuits

   • Found in electronic systems

detailed temporal structure of the response pattern

Number of action potentials per unit time

Signal transmission from neuron to neuron

• how effectively a synapse passes a signal

visual system

> 10^11 neurons and <10^15 synapses

Level I : Detailed compartmental models

Level II: Reduced compartmental models

Level III: Single-compartment models

Level IV: Cascade Models

Level V: Black-box models

from biophysically realistic, analysis requires simulations, strong paramter dependence to mathematical understanding, quantitative network models and oversimpliefied here

• Found that action potentials arise from voltage-gated Na⁺ and K⁺ channels.

• Created the first mathematical model of an action potential (Hodgkin-Huxley model).

• Showed how ionic conductance changes over time to generate nerve signals.

• Work was based on the squid giant axon and voltage clamp experiments.

Rebound spikes: Action potentials that occur after inhibitory (hyperpolarizing) input ends; involve T-type Ca²⁺ channels.

(also calles actionpotential)

Depolarization block: A state where prolonged depolarization inactivates Na⁺ channels, blocking further spiking.

• Tsodyks & Markram model describes synapses with a finite pool of resources that are used and recovered over time, explaining short-term plasticity.

• Synaptic depression is a temporary reduction in synaptic strength due to depletion of neurotransmitter vesicles during repetitive firing.

• Recovery occurs over milliseconds to seconds, shaping how neurons communicate during bursts.

• linear filtering with negative feedback

• adaption od neuronal gain

• IV

• Salamander and rabbit retinal ganglion cells

• John O’Keefe discovered place cells in the hippocampus that fire when an animal is in specific locations.

• May-Britt and Edvard Moser discovered grid cells in the entorhinal cortex that fire in a hexagonal spatial pattern.

• Together, these cells form the brain’s internal GPS system for navigation.

• prominent environmental cues or landmarks.

• They help integrate external sensory information with the internal spatial map.

• Important for context-dependent spatial navigation and correcting errors in path integration.

• Specialized neurons located in the medial entorhinal cortex (MEC).

• Fire in a regular, hexagonal grid pattern as an animal moves through space.

• Form a lattice of active “firing fields” covering the environment.

• Help the brain determine position and movement in space (internal GPS).

• Work together with place cells in the hippocampus for navigation and spatial memory.

A method to estimate stimulus features (like direction or position) by combining the activity of many neurons.

Each neuron’s preferred direction is weighted by its firing rate to form a population vector that approximates the actual stimulus.Used in motor cortex and visual cortex to decode movements and perception

How a stimulus causes neural activity.

Predicting or estimating the stimulus from that activity.

Often mathematical tuning curves are used for this task

1. Von Mises tuning defines how strongly each neuron responds to a given position — it describes each neuron's preferred location and tuning width.

2. Poisson spiking models the variability in neural firing — spike counts are noisy, but centered around the tuning curve's expected rate.

3. Posterior decoding uses the tuning and observed spikes to estimate a probability distribution over positions, combining likelihood and prior knowledge.

4. Maximum Likelihood Estimation (MLE) chooses the position that makes the observed spikes most likely, without using a prior — a quick "best guess."

MLE: Choose the position that makes the observed firing pattern most likely (maximize P(r∣x)P(r∣x)).

Posterior: Combine prior knowledge and observed activity to estimate position using Bayes’ rule (P(x∣r)∝P(r∣x)⋅P(x)P(x∣r)∝P(r∣x)⋅P(x)).

Posterior gives a full probability map; MLE gives a single best guess.

Grid cells fire in a hexagonal 2D lattice pattern across physical space.

This 2D alignment is shared within each module

By combining different modules with different scales, the brain can estimate unique global positions.

• Grid-like patterns appear in non-spatial tasks, like time or sequences.

• Example: A rat learns a sequence of smells — grid-like activity tracks its progress.

• Shows grid cells can map abstract spaces, not just physical ones.

1. tight coupling: Experiment - Theory

2. Focus on concrete question/hypothesis

3. focus on one or few levels of description

Adaption

Phasic spiking

Tonic Spiking

Subthreshold oscillation

Chattering

Resonator

Integrator

Bistability